Similarly, one has
\({\hbox{\rm Ad\,}}\widetilde{V}_{\mathrm {c},\kappa }(\phi _{\mathrm {c}}(f\oplus g)) = {\hbox{\rm Ad\,}}\widetilde{V}_{\mathrm {c},\kappa }(\phi _{\mathrm {c}}(2\Re f)\otimes {\mathbb {1}} - {\mathbb {1}}\otimes \phi _{\mathrm {c}}(2\Im f))\) 
From this one easily shows that the wedge algebra generated by the Zamolodchikov-Fadeev
fields in the sense of [1]} is equal to \(\widetilde{\mathcal {M}}_{\mathrm {c},\kappa }= \mathcal {M}_{\mathrm {c}}\otimes {\mathbb {1}} \vee {\hbox{\rm Ad\,}}\widetilde{V}_{\mathrm {c},\kappa }({\mathbb {1}}\otimes \mathcal {M}_{\mathrm {c}})\) .
